CN102809364B  Method for determining complex curved surface profile error  Google Patents
Method for determining complex curved surface profile error Download PDFInfo
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 CN102809364B CN102809364B CN201210236183.8A CN201210236183A CN102809364B CN 102809364 B CN102809364 B CN 102809364B CN 201210236183 A CN201210236183 A CN 201210236183A CN 102809364 B CN102809364 B CN 102809364B
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Abstract
Description
Technical field
The present invention relates to complexcurved error evaluation field, relate in particular to a kind of method of determining complexcurved profile error.
Background technology
In fields such as AeroSpace, shipbuilding and auto industrys, many important parts are often made up of the free profile of high precision, lifespan and the security of these parts to whole equipment plays an important role, so free form surface is being played the part of more and more important role in engineering reality, due to the process complexity of free form surface, processing cost is too high, so its error evaluation process is had to higher requirement, require to evaluate exactly wraparound error as far as possible, make it approach true error, give up to reduce production costs by avoiding by mistake.
In NC Machining Process, the classic method that workpiece is measured will be used various conventional measurers (clock gauge and slide calliper rule etc.) or equipment (three coordinate measuring machine etc.).For simple geometric measurement, operator can be directly with gage measuring on numericallycontrolled machine; For the measurement problem of the more complicated such as geometric properties or locus of workpiece, because conventional measurer cannot solve, operator must carry out workpiece transfer to three coordinate measuring machine.But while using this measuring method, will carry workpiece, the sequence of operations such as clamping and location again, tend in the meantime produce error, this can exert an influence to real error, reduces the efficiency of evaluation.
On the other hand along with CAD/CAM/CAI(computer aided design/computer aided machine/computer aided detection) development and machining precision from micron to nano level raising, GPS(product geometric sense technical manual) also there is huge variation in system.New generation of GPS is by the comprehensive call that provides emphatically to be suitable for every technology such as CAX(CAD/CAM/CAI) the integration environment, the geometric tolerances definition of clear and definite, system specifications more.Its most outstanding feature be exactly emphasize with mathematical method to the geometric error of product be described, definition, modeling and information transmission.The research of the mathematical definition theory to tolerance is carried out early in the U.S., and has promulgated first tolerance mathematical definition standard in the world.
How accurately to obtain profile error value and depend on concisely reasonably error model and fast and effeciently optimized algorithm, in recent years, scholar both domestic and external for provide various geometric configuratioies tolerance mathematical definition, set up profile error mathematical model, find efficiently fast optimized algorithm all made further investigation, for example:
(1) U.Roy and B.Li studied form and position tolerance mathematical modeling (referring to Roy U, Li B, for annotation and the expression of polytopic plants geometric tolerances (1. form tolerance), Computer Aided Design, 1998,30 (2): 151～161.)
(2) University Of Tianjin studied the mathematical definition of sphericity, complex position degree tolerance and error model (referring to He Gaiyun. the approximation theory of morpheme error and algorithm research [D]. Tianjin: University Of Tianjin, 2006.)
(3) Cai Min, poplar by the mathematical model of having studied CYLINDRICAL FEATURE such as new (referring to Cai Min, poplar by new etc., the research [J] of the CYLINDRICAL FEATURE mathematical model based on mathematical definition. mechanical engineering journal, 2003,39 (12): 86～90)
(4) Jiang Guohua etc. has studied cylindricity and has wanted geometric error evaluation algorithm, by conic projection on plane, so the evaluation of deviation from cylindrical form is converted into the evaluation of deviation from circular from, rotational plane again, obtain minimum error amount (referring to S.Hossein, Guohua Jiang, etal, evaluation [J] the .Precision Engineering of cylinder key element geometric properties, 2003,27 (2): 195～204)
(5) Zhu Limin etc. has been set up the mathematical model of point to curved surface directed distance, and has obtained function the second Taylor series formula by the method for difference, and is optimized taking expansion as objective function, thereby obtains error amount to be asked.(referring to Limin Zhu, Zhenhua Xiong, etal, complexcurved location based on distance function and profile error assessment method [J] .Journal of Manufacturing Science and Engineering, 2004,126 (3): 542～554), (Li Min Zhu, Xiao Ming Zhang, etal, the geometric meaning of signed distance function with and application [J] in curved surface approaches, Journal of Computing and Information Science in Engineering, 2010,10 (4): 110)
(6) Liao's equality has been set up point based on cutting apart approximation theory to complexcurved distance model, and has evaluated complexcurved profile error by genetic algorithm.(referring to Liao Ping, based on genetic algorithm with cut apart the complexcurved profile error of approximatioss accurate Calculation [J]. mechanical engineering journal, 2010,46 (10): 1～7)
(7) set up complexcurved thick coupling location model based on rigid motion theory under Euclidean Norm (referring to Xu Yi, Li Zexiang, the matching detection new method [J] of free form surface. Harbin Institute of Technology's journal, 2010,42 (1): 106～108), (Liu Yuanpeng, Liu Jing etc., complexcurved measurement data optimum matching problem research [J], China Mechanical Engineering, 16 (12): 1080～1082)
(8) how Wen Xiulan has studied and to have solved flatness and Linear Error (referring to Xiulan Wen by genetic algorithm, Aiguo Song, for the improved genetic algorithm of one [J] the .International Journal of Machine Tools & Manufacture of Evaluation plane degree and straightness error, 2003,43 (11): 1157～1162)
Inventor is realizing in process of the present invention, finds at least to exist in prior art following shortcoming and defect:
Abovementioned achievement in research major part has only been set up the error evaluation of simple profile, though some has completed complexcurved error evaluation, but the error amount assessing is far longer than given tolerance range, causes workpiece mistake rate higher, has improved production cost.
Summary of the invention
The invention provides a kind of method of determining complexcurved profile error, the present invention has reduced workpiece mistake rate and production cost, described below:
A method of determining complexcurved profile error, said method comprising the steps of:
(1) the survey termination of contact threedimensional gauge head contacts the digital control system of sending trigger pip after surface of the work and send to by signal receiving device machining center, the current coordinate position latch that described contact threedimensional gauge head is surveyed end by described digital control system is got off, and sends described current coordinate position to data processing terminal;
(2) described data processing terminal is set up complexcurved profile error model by described current coordinate position;
(3) described data processing terminal, by measuring the thick coupling of coordinate system and design coordinate system, obtains the pose initial parameter of ideal surface;
(4) described data processing terminal obtains complexcurved profile tolerance initial error by described pose initial parameter and described complexcurved profile error model;
(5) described data processing terminal is optimized described pose initial parameter, and again execution step (4), obtain complexcurved profile tolerance error current, until the difference of described complexcurved profile tolerance error current and described complexcurved profile tolerance initial error is while being less than threshold value, using described complexcurved profile tolerance error current as complexcurved profile tolerance final error and output.
Described data processing terminal is set up complexcurved profile error model by described current coordinate position and is specifically comprised:
1) described data processing terminal obtains complexcurved profile tolerance tolerance range;
Wherein, p point is measurement point, and q point is mathematical point, n ^{q}the normal vector that represents q on ideal surface, t is tolerance value;
2) described data processing terminal is set up described complexcurved profile error model by described complexcurved profile tolerance tolerance range;
Wherein, any one complexcurved around x, y, the angle of z axle rotation is respectively α, beta, gamma; Along x, y, the translational movement of z axle is δ _{x}, δ _{y}, δ _{z}; The coordinate of measurement point p is (x _{p}, y _{p}, z _{p}), the coordinate of mathematical point q is (x _{q}, y _{q}, z _{q}), normal vector n ^{q}coordinate be
Described data processing terminal obtains complexcurved profile tolerance initial error by described pose initial parameter and described complexcurved profile error model and is specially:
Described data processing terminal is brought into described pose initial parameter in described complexcurved profile error model and gets the ultimate range of described measurement point p to described ideal surface, using the ultimate range of 2 times as described complexcurved profile tolerance initial error.
The beneficial effect of technical scheme provided by the invention is: this method, by pose initial parameter is optimized, is obtained complexcurved profile tolerance error current; In the time that difference is less than threshold value, the also output using complexcurved profile tolerance error current as complexcurved profile tolerance final error; The final error getting by this method approaches given tolerance range, has reduced workpiece mistake rate and production cost, has improved accuracy of detection.
Brief description of the drawings
Fig. 1 is the structural representation of machining center provided by the invention;
Fig. 2 is the process flow diagram of a kind of method of determining complexcurved profile error provided by the invention.
Embodiment
For making the object, technical solutions and advantages of the present invention clearer, below in conjunction with accompanying drawing, embodiment of the present invention is described further in detail.
In order to reduce workpiece mistake rate and production cost, the embodiment of the present invention provides a kind of method of determining complexcurved profile error, referring to Fig. 1 and Fig. 2, described below:
101: the survey termination of contact threedimensional gauge head contacts the digital control system of sending trigger pip after surface of the work and send to by signal receiving device machining center, the current coordinate position latch that contact threedimensional gauge head is surveyed end by digital control system is got off, and sends current coordinate position to data processing terminal;
As shown in Figure 1, contact threedimensional gauge head is arranged on machine tool chief axis by the taper shank of standard.The connection of the two is very easy, but it should be noted the centering of gauge head and mainshaft axis.The major function of contact threedimensional gauge head is to adopt a little at surface of the work, after the survey termination of contact threedimensional gauge head contacts surface of the work, sends trigger pip and sends signal receiving device to.Signal receiving device is arranged on the appropriate location of machining center, and the trigger pip of sending for receiving contact threedimensional gauge head carries out trigger pip being sent to after necessary signal condition the digital control system of machining center.Owing to carrying out signal transmission with infrared mode between contact threedimensional gauge head and signal receiving device, so need to consider not stop in the course of work of machining center the signal transmission between Contacting three coordinates measurement gauge head and receiving trap when signal receiving device is installed.Signal receiving device send to machining center digital control system be only contact threedimensional gauge head touch surface of the work produce trigger pip, digital control system receives the servodrive system stop motion at controlled working center immediately after trigger pip, and the current coordinate position latch that the contact threedimensional gauge head that is arranged on machining center main shaft place is surveyed end is got off.Digital control system receives the information of the point of the needs measurement transmitting by communication line on the one hand, sends the geological information of the surface of the work point of having measured to data processing terminal on the one hand.
102: data processing terminal is set up complexcurved profile error model by current coordinate position;
Wherein, this step specifically comprises:
1) data processing terminal obtains complexcurved profile tolerance tolerance range;
Refer to that for complexcurved key element profile tolerance tolerance range diameter equals tolerance value t, the centre of sphere is positioned at the region that two enveloping surfaces of a series of balls on ideal surface S limit, so find, in space, some the distance function to tested curved surface key element is most important, Euclidean distance d (the p of nearest any of what point can be similar to the distance of ideal surface S be expressed as this point of distance on point to curved surface, S)
d(p,S)=‖pq‖ _{2}
Wherein, the point that q point is upper for ideal surface S and p point is nearest, p point is measurement point, q point is mathematical point.
Further, by d (p, S) linear parsing at q point place
d(p,S)≈d(q)+▽d(q) ^{T}·(pq)
Wherein d (q) represents the distance of some q to ideal surface S, ▽ d (q) ^{t}represent the Grad of d (p, S) function at q.The eikonal equation(eikonal equation of introducing) be the nonlinear partial differential equation running into during ripple is propagated, there is following form  ▽ u (x) =F (x), x ∈ Ω, Ω is R ^{n}in (n ties up real number space), be communicated with open region, F (x) is the Positive Function of input, and ▽ refers to gradient,  represent European norm, represent the border of Ω.Physically, what the solution u of equation (x) represented is the beeline from the border of Ω to Ω internal point, and in the time of F=1, what this separated representative is the directed distance from Ω border to Ω inside.If d is (p, S) be u (x), can be using the outside ideal surface border as being communicated with open region Ω, ▽ d (q, S)=1, d (q, S)=0, the solution of d (p, S) is the outer beeline that a bit arrives ideal surface S of ideal surface so, note ▽ d (q, S)=1=n ^{q}, n ^{q}the normal vector that represents q on ideal surface, can be expressed as d (p, S)=(pq) n to the signed distance function of ideal surface S so ^{q}.If measurement point p is in tolerance range, this measurement point p should meet t is as implied above, representative be tolerance value, this formula can be defined as to complexcurved profile tolerance tolerance range.
2) data processing terminal is set up complexcurved profile error model by complexcurved profile tolerance tolerance range.
In the time that the pose of ideal surface S changes, while being rotated translation motion, the mathematical point q corresponding with ideal surface S external pelivimetry point p also can change.
If one is complexcurved around x, y, the angle of z axle rotation is respectively α, beta, gamma, along x, y, the translational movement of z axle is δ _{x}, δ _{y}, δ _{z}, ω=[α, beta, gamma], v=[δ _{x}, δ _{y}, δ _{z}], volume coordinate rotation matrix is;
Work as α, beta, gamma is enough little, utilizes Taylor expansion formula to omit higher order term, can obtain the approximate matrix R of R ^{*}
For convenience of calculating, introduce matrix, that is:
R
^{*}can be reduced to
Provable: x is vectorial arbitrarily
If curved surface just carries out small variation, translation and rotation can be expressed as signed distance function when all very little
Its representative be point to the signed distance function of movement curved surface, utilize calculus of differences can obtain the single order differential term of signed distance function, the paper of mentioning in itself and technical background (5) is made comparisons:
In the model of paper, the line of p and q is and n ^{q}the line segment paralleling, so Section 2 is zero in above formula, and because rotation translational movement is very little, item more than second order can be ignored, so above formula becomes
This has just obtained and result same in paper, has proved the correctness of model, using the signed distance function with rotation translational movement as objective function.After formula is arranged, obtaining signed distance function differential expressions is:
Mathematical model using above formula as Evaluating Profile Error of Complex Surfaces.
Wherein, the coordinate of measurement point p is (x _{p}, y _{p}, z _{p}), the coordinate of mathematical point q is (x _{q}, y _{q}, z _{q}), normal vector n ^{q}coordinate be
103: data processing terminal, by measuring the thick coupling of coordinate system and design coordinate system, obtains the pose initial parameter of ideal surface;
Because measurement point in model and mathematical point are under the same coordinate system, thus need two processes for the evaluation of complexcurved profile error, the one, need to align with design coordinate system measuring coordinate system, to eliminate the errors of bringing due to coordinate system difference; The 2nd, thus utilize optimized algorithm error model to be optimized to the result that obtains evaluation.
Align for coordinate system, i.e. thick coupling, take the coordinate matching method based on unique point, because matching process does not change the inherent geometric properties of measuring curved surface or ideal surface, so can regard rigid body as by measuring curved surface or ideal surface, rotary flat shifting movement is as rigid motion, rigid motion does not change the result of inner product and apposition computing, so the distance of measuring on curved surface or ideal surface between points can not change because the generation of rotation translation, so just can extract unique point, P, Q represents respectively to measure point set and theoretical point set, O (x _{lz}, y _{lz}, z _{lz}) mid point of representation theory point set Q, O ' (x _{cz}, y _{cz}, z _{cz}) represent that the mid point idiographic flow of measurement point set P is as follows:
1) get theoretical point set Q and the coordinate of measuring point set P mid point;
Wherein, p _{i}represent to measure the arbitrfary point in point set P, q _{i}arbitrfary point in representation theory point set Q.
2) in whole theoretical point set Q and measurement point set P, the nearest point of detection range mid point is put p as First Characteristic respectively _{tz1}, q _{tz1};
3) ergodic theory point set Q finds respectively with First Characteristic point distance point farthest and puts p as Second Characteristic with measurement point set P _{tz2}, q _{tz2};
4) ergodic theory point set Q finds respectively with Second Characteristic point distance point farthest respectively as the 3rd unique point p with measurement point set P _{tz3}, q _{tz3};
5) taking three unique points as Foundation local coordinate system:
The Xaxis of two local coordinate systems is respectively:
yaxis is
6) pass through can determine the rotation matrix that is tied to design coordinate system from measuring coordinate, then pass through K=p _{tz1}q _{tz1}r, can determine translation vector.
Pass through abovementioned steps, can complete and measure coordinate system and design aliging of coordinate system, after thick coupling, measuring point set P and theoretical point set Q is in little deviation range, meet the requirement to parameter area in model completely, in meticulous coupling below, just carry out error evaluation using the complexcurved profile error model of setting up as objective function above.The process of abovementioned thick coupling, for conventionally known to one of skill in the art, when specific implementation, can also adopt other thick matching process, and the embodiment of the present invention does not limit this.
104: data processing terminal obtains complexcurved profile tolerance initial error by pose initial parameter and complexcurved profile error model;
This step is specially: pose initial parameter is brought in complexcurved profile error model and gets the ultimate range of measurement point p to ideal surface S, using the ultimate range of 2 times as complexcurved profile tolerance initial error.
105: data processing terminal is optimized pose initial parameter, and again perform step 104, obtain complexcurved profile tolerance error current, until the difference of complexcurved profile tolerance error current and complexcurved profile tolerance initial error is while being less than threshold value, using complexcurved profile tolerance error current as complexcurved profile tolerance final error and output.
Wherein, the embodiment of the present invention gets complexcurved profile tolerance final error by continuous iteration, and threshold value is set according to the needs in practical application, and when specific implementation, the embodiment of the present invention does not limit this.
Wherein, data processing terminal is optimized as conventionally known to one of skill in the art pose initial parameter, can adopt multiple optimization method to realize, and the embodiment of the present invention does not repeat at this.
Verify the feasibility of a kind of method of determining complexcurved profile error that the embodiment of the present invention provides below with concrete test, described below:
In order to verify the validity of abovementioned model, design is experiment as follows, taking the worm toothsurface often used in producing and ellipsoid as example, describes.
Two kinds of curved surfaces are carried out respectively to 5 groups, amounted to 10 groups of experiments, respectively two measurement points have been added to (0 of Normal Distribution, 0.004), (0,0.005), (0,0.006), (0,0.007), (0,0.008) stochastic error is similar to mismachining tolerance, evaluates respectively by this method and least square method, as shown in the table:
The error amount that this method assesses is significantly less than the error amount that least square method assesses, and so just can approach actual tolerance range, obtains real error amount, obtains high accuracy of detection, and the manufacturer of making a living provides real examining report, reduces the useless rate of mistake and production cost.
In sum, the embodiment of the present invention provides a kind of method of determining complexcurved profile error, and this method, by pose initial parameter is optimized, is obtained complexcurved profile tolerance error current; In the time that difference is less than threshold value, the also output using complexcurved profile tolerance error current as complexcurved profile tolerance final error; The final error getting by this method approaches given tolerance range, has reduced workpiece mistake rate and production cost, has improved accuracy of detection.
It will be appreciated by those skilled in the art that accompanying drawing is the schematic diagram of a preferred embodiment, the invention described above embodiment sequence number, just to describing, does not represent the quality of embodiment.
The foregoing is only preferred embodiment of the present invention, in order to limit the present invention, within the spirit and principles in the present invention not all, any amendment of doing, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.
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